Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect

Abstract

The ladder operators in harmonic oscillator are a well-known strong tool for various problems in physics. In the same sense, it is sometimes expected to handle the problems of repulsive harmonic oscillator in a similar way to the ladder operators in harmonic oscillators, though their analytic solutions are well known. In this paper, we discuss a simple algebraic way to introduce the ladder operators of the repulsive harmonic oscillators, which can reproduce well-known analytic solutions. Applying this formalism, we discuss the charged particles in a constant electric field in relation to the Schwinger effect; the discussion is also made on a supersymmetric extension of this formalism.

18pages, 3figures

References in corpus (1)

• Inverting a normal harmonic oscillator: Physical interpretation and applications

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• Bi-local fields interacting with a constant electric field and related problems including the Schwinger effect